If \(a+b\) means \(a-b\), \(a-b\) means \(a \times b\), \(a \times b\) means \(a/b\), \(a/b\) means \(a+b\), then what is the value of \(10+30-100\times50/25\)?
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In operator replacement problems:
Always substitute symbols first, then apply BODMAS.
Never solve directly without replacing operators.
Step 1: Rewrite each operator using its new meaning. Replace every symbol in the expression with the operation it has been redefined to mean, in place of its usual one. Step 2: Substitute into the given expression. Apply the swapped meanings to 10+30-100 times 50/25 term by term. Step 3: Solve following the correct order of operations. Carrying out the substituted operations in sequence and simplifying gives the final value. \[ \boxed{-25} \]